Q) Here is a problem from MEP Year 9 book. It is question 5: "The diagram shows how the sign that hangs over the Fish and Chip shop is suspended by a rope and a triangular metal bracket. Find the length of the rope."
I include two solutions. Solution 1 is how I would have done it and most pupils did it this way.
The problem arose when a pupil used Solution 2 and got a different answer.
Both solutions look correct. Is there something in the question that causes this?
Solution 1 Solution 2
A) Your methods are correct if the angles are right angles, as your students' solutions imply; it is these assumptions that are wrong. Creating questions is tricky and mistakes can be made, which in this case is a question that doesn't contain enough information.
The first assumption that has been made by all the pupils is that the triangular metal bracket holding the board is a right-angled triangle; it actually doesn't say this anywhere. I used PowerPoint and straight lines to recreate the diagram in Solution 2. If you draw this then the angle made with the rope and metal bracket is not a right angle, so Pythagoras cannot be used.
The diagram given in the question clearly says this is a right angle. This must imply, therefore, that the metal bracket is not a right-angled triangle, so the question does not contain enough information to give an answer.
I suggest that your pupils try constructing these triangles using a compass, ruler and pencil, PowerPoint or a geometry software package.
Q) When multiplying or dividing by 10, 100 or bigger, the teacher tells her pupils to move the figures, not the decimal point. I am a teaching assistant and was always taught to move the decimal point. I think it is far easier, because you can easily count with your pencil moving over the numbers to get the point in the right place. Am I wrong?
A) Until about six years ago, I always taught "move the decimal point" and would happily bounce my pencil along the digits to get the correct answer when multiplying by powers of 10. I used to do the same demonstration using digit cards - it was much easier to move the decimal point than to try and shift all the digits. Then I was running a workshop and one of the delegates told me off. Correctly speaking, it is the digits that move and since that workshop this is what I have taught to make sure that students fully understand the concept. For those who still find it difficult, we move the decimal point. As long as place value is understood, any sound technique we employ to get the answer correct is fine.
There is a discussion on The TES maths forum about this question: www.tes.co.uksectionstaffroomthread.aspx?story_id=2161205path=mathemati csthreadPage=1 We have also created an interactive Flash program using a lorry, so you and your pupils see what happens. They could use their whiteboards and you could then click to demonstrate the answer. This is available on www.mathagonyaunt.co.uk